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Computational chemistry

Dances with hydrogen cations

Nature volume 457, pages 673674 (05 February 2009) | Download Citation

Life depends on the flow of hydrogen cations in water, yet their dynamic behaviour when in complex with water molecules is unknown. The latest computer simulations cast light on the jiggling of these hydrated ions.

In water, hydrogen cations (H+) abound, but they exist only as complexes with water molecules. One of the most important of these complexes is the Zundel cation, in which a hydrogen cation is shared by two water molecules. The structure of the Zundel cation has been known for years, owing to evidence from infrared (IR) spectra. But its dynamic behaviour — how the hydrogen cation moves between the two water molecules — is unknown. In Angewandte Chemie, Vendrell et al.1 report accurate computer simulations of the IR spectrum of the Zundel ion in the gas phase, and of analogues in which hydrogen atoms have been replaced with deuterium atoms. This allows the first complete characterization of the complex molecular vibrations of Zundel ions, providing information that might contribute to a long-sought-after goal — an accurate computational model of how hydrogen ions are transported through liquid water.

Hydrogen cations are ubiquitous in nature, and are vital components of many chemical and biological environments. For example, they take part in acid–base reactions that determine the formation, fate and transport of the main environmental pollutants that cause acid rain; they are pumped across cell membranes by dedicated proteins, creating gradients in pH and charge that act as energy reservoirs for the cell; and hydrogen-ion movement, when coupled to electron transfer in enzymes, allows bioenergetic conversions to occur, and 'activates' enzyme substrates, readying them to take part in catalytic bond-breaking and bond-making reactions.

Curiously, hydrogen cations seem to diffuse faster through water than do other atomic cations. In fact, hydrogen-cation 'diffusion' in water involves the concerted making and breaking of many bonds in networks of water molecules, in a process known as the Grotthuss mechanism2 (Fig. 1a). When a hydrogen cation forms a bond to a water molecule, other covalent and hydrogen bonds throughout the network break and re-form until a different hydrogen ion is ejected. Hydrogen cations in water are thus hydrated: they either exist in complex with individual water molecules, forming Eigen ions3 (H3O+), or are shared equally by two water molecules to form Zundel ions4 (H2O–H–H2O)+. The exact form taken by hydrated hydrogen ions — known collectively as hydronium ions — has long received much attention5,6,7.

Figure 1: The Zundel cation and its vibrations.
Figure 1

a, Hydrogen ions (H+) move through water by the Grotthuss mechanism, in which hydrogen bonds (dashed lines) and covalent bonds (solid lines) between water molecules are broken and re-formed. The mechanism can involve any number of water molecules, but only four are shown here for simplicity. b–d, The Zundel cation is the smallest structural unit that enables the sharing of a hydrogen ion by two water molecules. Its modes of vibration include stretches of the outer oxygen–hydrogen bonds (b), internal bending of the water molecules (c), and vibrations between the water molecules and the hydrogen ion (d). Vendrell et al.1 compute the infrared spectra of Zundel cations, and of analogues of the ions in which one or more hydrogen atoms have been replaced with deuterium atoms. The different degrees of coupling between vibrational modes in each analogue produce complex spectra, which reflect the different dynamics of each analogue.

Aqueous hydronium clusters are considered to be effective vehicles for probing the dynamic environment of hydrogen cations in more complex systems such as liquid water8,9. The IR spectra of hydronium ions (and of their deuterium-containing analogues) can be thought of as 'fingerprints' of the underlying molecular structure and of the dynamics of the ions' hydrogen-bonding network. The correlation10,11 between the IR spectrum and the structure of each ion provides a method for identifying the ions' structures, and yields information about the coupling between the various vibrational modes of the ions.

But the dynamic behaviour and complex vibrational motions of hydronium ions are by no means obvious. The simple harmonic picture of vibrations (which assumes that atoms behave as frictionless masses connected by springs) is valid only around the equilibrium positions of the atoms; in Zundel cations, IR spectra instead suggest the existence of large-amplitude, anharmonic motions. The presence of Fermi resonances — overlapping absorption lines that arise from strong couplings between vibrational states of similar energies — in the IR spectra of Zundel cations also makes it difficult to work out the dynamic behaviour of the ions from the spectra. Several approaches12,13 have therefore been introduced to account for the Fermi resonances and to describe large-amplitude molecular motions.

A good way to validate the theoretical approaches and to refine structural models of hydronium ions is to compute the IR spectra that would be obtained from an assumed structure, and then to compare these spectra with experimental data. Vendrell et al.1 computed the IR spectra for the Zundel cation by integrating the ion's vibrational, time-dependent Schrödinger equation in 15 dimensions — one dimension for each vibrational degree of freedom — using a 'wavefunction propagation' approach14. This required an analytical description of the potential energy surface of the cation to describe the total energy of the system as a function of each degree of freedom. The authors thus obtained spectra for the Zundel ion itself, and for the deuterium-containing ions D(D2O)2+, H(D2O)2+ and D(H2O)2+ (where D is deuterium). They found that increasing the number of deuterium ions in the Zundel ion progressively complicates the spectrum — creating a bigger “mess”, to use the authors' own word.

Perhaps unsurprisingly, Vendrell and colleagues' computed spectra show that the vibrations of 'free' oxygen–hydrogen bonds — those containing hydrogen atoms that don't participate in hydrogen bonding (Fig. 1b) — are broadly unaffected when their hydrogen atoms are replaced with deuterium atoms. The only effect of deuteration is a shift of the relevant peaks towards lower frequencies, as would be expected from the change in mass associated with the substitution. By contrast, the peaks of the spectra associated with internal bending of the water molecules (Fig. 1c), and with vibrations of the bonds and atoms that form hydrogen bonds (Fig. 1d), vary dramatically with deuteration of the ions.

Vendrell and colleagues' approach allows the various peaks in the spectra to be precisely explained in terms of combinations of the constituent vibrational modes of Zundel ions. They thus show that the complicating effects of deuterium atoms on the dynamics of Zundel ions depend on which hydrogens within the cluster they replace. To be precise, the presence of deuterium in the water molecules induces strong couplings between the movements of the central hydrogen ion and the water molecules. Conversely, when the hydrogen ion is replaced with a deuterium ion, these motions are decoupled and the resulting spectra are simpler than those of non-deuterated Zundel ions.

This work1 is the first step in obtaining a quantitative picture of the complex dynamics associated with the interactions of hydrogen cations with water. It is a great start, but there is still a long way to go. The spectra of hydrogen ions that have more water molecules9 must now be analysed for us to understand how such spectra evolve with cluster size, and to unravel the role of the collective effects that facilitate the Grotthuss mechanism in liquid water. The potential energy surfaces of such clusters have more degrees of vibrational freedom than Zundel ions, making it more difficult both to obtain an analytical description of each cluster, and to solve the time-dependent Schrödinger equation in all dimensions. New theoretical approaches will therefore be needed to address these issues, and to deal with possible strong couplings between different vibrational modes in many dimensions, which would produce even more complex spectra. Alternatively, simpler descriptions of the underlying intermolecular interactions between hydrogen cations and water can be sought6,15, in which case Vendrell and colleagues' approach will provide the machinery to fit those descriptions so that they can reproduce experimental spectra.

Obtaining an accurate description of the interactions between water molecules (or between water molecules and ions), and understanding the collective physical phenomena that are present in water, will result in better models of the liquid that can be used to study solvation and reactions in aqueous environments. This will ultimately offer molecular-level insight into important environmental processes — such as the fate and transport of contaminants in rivers and aquifers — and decipher the function of water in confined spaces of biological interest.


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  1. Sotiris S. Xantheas is in the Chemical and Materials Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, USA.

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